Grinberg, N. I. On Poisson brackets of hydrodynamic type with degenerate metric. (Russian) Zbl 0611.58017 Usp. Mat. Nauk 40, No. 4(244), 217-218 (1985). It is established that for reducing the metric tensor \((g^{ij})\) with degeneration of the constant rank m, rank \(g^{ij}=m\leq n\), to the form \(g^{ij}\equiv const\) by local transformations it is necessary for the system in question to be the Poisson brackets. The cases \(m=n-1\), n-2 and other examples are considered in detail. Reviewer: G.Il’jusina Cited in 8 Documents MSC: 53D17 Poisson manifolds; Poisson groupoids and algebroids 37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010) Keywords:metric tensor; local transformations; Poisson brackets PDFBibTeX XMLCite \textit{N. I. Grinberg}, Usp. Mat. Nauk 40, No. 4(244), 217--218 (1985; Zbl 0611.58017)